Model Simulations of a Shock-Cloud Interaction in the Cygnus Loop

We present optical observations and 2D hydrodynamic modeling of an isolated shocked ISM cloud. H$\alpha$ images taken in 1992.6 and 2003.7 of a small optical emission cloud along the southwestern limb of the Cygnus Loop were used to measure positional displacements of $\sim$ $0 \farcs 1$ yr$^{-1}$ for surrounding Balmer dominated emission filaments and $0\farcs025 - \farcs055$ yr$^{-1}$ for internal cloud emission features. These measurements imply transverse velocities of $\simeq$ 250 km s$^{-1}$ and $\simeq$ 80 -- 140 km s$^{-1}$ for ambient ISM and internal cloud shocks respectively. The complex shock structure visible within the cloud indicates that the cloud's internal density distribution is two phased: a smoothly varying background density which is populated by higher density clumps. We present model results for a shock interacting with a non-uniform ISM cloud. We find that this cloud can be well modeled by a smoothly varying power law core surrounded by a low density envelope with a Lorentzian profile. The lack of sharp density gradients in such a model inhibits the growth of Kelvin-Helmholtz instabilities, consistent with the cloud's appearance. Our model results also suggest that cloud clumps have densities $\sim$ 10 times the ambient ISM density and account for $\sim$ 30% of the total cloud volume. Moreover, the observed spacing of internal cloud shocks and model simulations indicate that the distance between clumps is $\sim$ 4 clump radii.